Flow control coefficients

Steady-state metabolic flows./ depend on the total concentrations of the enzymes Ek, and flow control coefficients ( jj are defined by... 

The flow control coefficients relate the fractional changes in the steady-state flows to the changes in the total enzyme concentrations. The partial derivatives of reaction rates JT ] with respect to the substrate concentrations Sj are called the elasticity coefficients e,y, and given by... 

The determination of flow control coefficients is difficult, and requires the independent variation of the activity of all the enzymes within the pathway. Based on linear nonequilibrium thermodynamics, the kinetics of enzyme reactions can be described by the linear functions of the change in Gibbs free energy. This yields a direct relation between the elasticity coefficients and the change in Gibbs free energy for the reactions in a simple two-step pathway. 

The metabolic control analysis can be used to study diseases caused by enzyme functions or dysfunctions, and helps us to understand certain pathways. It may be critical in determining the enzymes with the highest flow control coefficient, in order to inhibit or control enzyme functions. This may lead to the quantification of rate limitations in... 

Characterization and influence of electrohydro dynamic secondary flows on convective flows of polar gases is lacking for most simple as well as complex flow geometries. Such investigations should lead to an understanding of flow control, manipulation of separating, and accurate computation of local heat-transfer coefficients in confined, complex geometries. The typical Reynolds number of the bulk flow does not exceed 5000. 

Now it appears that the value of may be estimated by using the loss coefficient K determined at choking provided K is not too small. This is unlikely since in most valves effective flow control occurs at very small throat area when the valve is in the 10-30% open range. The loss coefficient is determined from the pressure loss across the valve and the velocity in the upstream pipe at choking. 

Liquid fertilizers, potassium orthophosphates in, 20 637 Liquid-film coefficient, 15 695 Liquid filtration, 11 322-323 Liquid flavor forms, 11 576-577 Liquid flow control, in variable-conductance heat pipes, 13 233 Liquid fluidization, 11 791-792 Liquid food ingredients, encapsulated,... 

C, for each enzyme in a pathway. This coefficient expresses the relative contribution of each enzyme to setting the rate at which metabolites flow through the pathway—that is, the flux, J. C can have any value from 0.0 (for an enzyme with no impact on the flux) to 1.0 (for an enzyme that wholly determines the flux). An enzyme can also have a negative flux control coefficient. In a branched pathway, an enzyme in one branch, by drawing intermediates away from the other branch, can have a negative impact on the flux through that other branch (Fig. 15-34). C is not a constant, and it is not... 

Figure 3.14. The lower ends of fractionators, (a) Kettle reboiler. The heat source may be on TC of either of the two locations shown or on flow control, or on difference of pressure between key locations in the tower. Because of the built-in weir, no LC is needed. Less head room is needed than with the thermosiphon reboiler, (b) Thermosiphon reboiler. Compared with the kettle, the heat transfer coefficient is greater, the shorter residence time may prevent overheating of thermally sensitive materials, surface fouling will be less, and the smaller holdup of hot liquid is a safety precaution, (c) Forced circulation reboiler. High rate of heat transfer and a short residence time which is desirable with thermally sensitive materials are achieved, (d) Rate of supply of heat transfer medium is controlled by the difference in pressure between two key locations in the tower, (e) With the control valve in the condensate line, the rate of heat transfer is controlled by the amount of unflooded heat transfer surface present at any time, (f) Withdrawal on TC ensures that the product has the correct boiling point and presumably the correct composition. The LC on the steam supply ensures that the specified heat input is being maintained, (g) Cascade control The set point of the FC on the steam supply is adjusted by the TC to ensure constant temperature in the column, (h) Steam flow rate is controlled to ensure specified composition of the PF effluent. The composition may be measured directly or indirectly by measurement of some physical property such as vapor pressure, (i) The three-way valve in the hot oil heating supply prevents buildup of excessive pressure in case the flow to the reboiier is throttled substantially, (j) The three-way valve of case (i) is replaced by a two-way valve and a differential pressure controller. This method is more expensive but avoids use of the possibly troublesome three-way valve.

Control valves. Valve vendors publish much information about flow-control valves. Much of their information covers what is known as control valve flow coefficients Cv. It is convenient to express the valve capacity and the valve flow characteristics in terms of the flow coefficient Cv. This value is defined as the flow of water at 60°F, in gallons per minute (gpm), at a pressure drop of 1.0 psi across the valve. In a flow valve, therefore, controlling the flow of water at 60°F as the valve opens, keeping a 1.0-psi pressure drop across the valve, the C value is the rate of water flow, gpm. 

The control systems enabled in the simulation were i) the IHX flow balance controller, which acts through primary compressor speed to maintain equal flow rate on the hot and cold sides of the IHX ii) the bypass flow controller which acts through bypass valve loss coefficient to maintain a shaft speed set point. Additionally the pre-cooler and intercooler cold side flow rates are supplied as forcing functions. The flow rates were roughly matched to decay heat level. The PCU shaft set point is decreased from 60 Hz over time to have the shaft speed more or less track the decreasing reactor energy production rate. 

The metabolic control analysis determines quantitatively the effects of various metabolic pathway reactions on flows and on metabolic concentrations. The analysis defines two coefficients (i) the control coefficients, which characterize the response of the system flows, concentrations, and other variables after parameter perturbations and (ii) the elasticity coefficients, which quantify the changes of reaction rates after perturbations of substrate concentrations or kinetic parameters under specified conditions. 

The flow or concentration control coefficients are related to elasticity coefficients through the conservation relations and connectivity theorems. 

Here, the coefficients expressing the control by the load process do not cany an asterisk superscript, since they are not overall control coefficients. Multiplying the nonnormalized control coefficients with the ratio of flows JJJp yields the normalized coefficients CJQ°, which satisfy the usual summation conditions (Schuster and Westerhoff, 1999)... 

Control coefficients related to slipping enzymes can be calculated by the linear nonequilibrium thermodynamics approach. The overall control coefficients in the modular approach describe the control exerted by the particular degrees of freedom of a module on the measurable variables at steady state. Using the degree of coupling q (qop = Z0p/ ZpZ0) and the phenomenological stoichiometry Z (Z = Zp/Z0), the reation flows of. /ro and. /rp in Eq. (11.47) become... 

These reservoirs realize the over-year (complete) regulation of the Syrdarya flow, the coefficient of control of total water resources reached a practically boundary value of 0.93. The main regulator of flow is Toktogul reservoir capable of realizing an over-year control of Naryn runoff and the compensated regulation of water resources of the middle and lower stream of the Syrdarya. 

Fillers are often useful in epoxy-polyamide adhesives (41). Fillers aid flow control—particularly at elevated temperatures. Other properties contributed by fillers are exhibited in the cured system. For example, they can increase the modulus of elasticity, modify the coefficient of thermal expansion, increase heat resistance, and even affect bond strength. Of course, the excellent wetting properties of polyamides Increase the dispersion efficiency of these fillers. The type of filler selected and the amount used also have a pronounced effect on adhesive quality. A few of these effects are illustrated in Tables VI and VII (37). (See also Table VIII.)... 

Bankoff [343] suggested that heat transfer coefficients in film boiling could be substantially improved by continuously removing vapor through a porous heated surface. Subsequent experimental work [344, 345] demonstrated that coefficients could be increased by as much as 150 percent, provided that a porous block was placed on the surface to stabilize the flow of liquid toward the surface. Wayner and Kestin [346] extended this concept to nucleate boiling and found that wall superheats could be maintained at about 3 K (5.4°F) for heat fluxes over 300,000 W/m2 or 95 x 103 Btu/(h-ft2). This work was extended by Raiff and Wayner [347], The need for a porous heated surface and a flow control element appears to limit the application of suction boiling. 

---